Choose the correct answer from the alternatives given :
If $a^{2} + b^{2} = 1, c^{2} + d^{2} = 2 t h e n (a c - b d)^{2} + (a d + b c)^{2}$ is

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Solution

The correct option is A 2
Given that,
$a^{2} + b^{2} = 1 a n d c^{2} + d^{2} = 2$
$(a c - b d)^{2} + (a d + b c)^{2}$
$= a^{2} c^{2} + b^{2} d^{2} - 2 a b c d + a^{2} d^{2} + b^{2} c^{2} + 2 a d b c$
$a^{2} c^{2} + a^{2} d^{2} + b^{2} d^{2} + b^{2} c^{2}$
$a^{2} (c^{2} + d^{2}) + b^{2} (d^{2} + c^{2})$
$a^{2} 2 + b^{2} 2 = 2 (a^{2} + b^{2})$
= 2 $\times$ 1 = 2

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